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Simplifying 7x + -4 = 5(x + 1)(2x + 3) Reorder the terms: -4 + 7x = 5(x + 1)(2x + 3) Reorder the terms: -4 + 7x = 5(1 + x)(2x + 3) Reorder the terms: -4 + 7x = 5(1 + x)(3 + 2x) Multiply (1 + x) * (3 + 2x) -4 + 7x = 5(1(3 + 2x) + x(3 + 2x)) -4 + 7x = 5((3 * 1 + 2x * 1) + x(3 + 2x)) -4 + 7x = 5((3 + 2x) + x(3 + 2x)) -4 + 7x = 5(3 + 2x + (3 * x + 2x * x)) -4 + 7x = 5(3 + 2x + (3x + 2x2)) Combine like terms: 2x + 3x = 5x -4 + 7x = 5(3 + 5x + 2x2) -4 + 7x = (3 * 5 + 5x * 5 + 2x2 * 5) -4 + 7x = (15 + 25x + 10x2) Solving -4 + 7x = 15 + 25x + 10x2 Solving for variable 'x'. Reorder the terms: -4 + -15 + 7x + -25x + -10x2 = 15 + 25x + 10x2 + -15 + -25x + -10x2 Combine like terms: -4 + -15 = -19 -19 + 7x + -25x + -10x2 = 15 + 25x + 10x2 + -15 + -25x + -10x2 Combine like terms: 7x + -25x = -18x -19 + -18x + -10x2 = 15 + 25x + 10x2 + -15 + -25x + -10x2 Reorder the terms: -19 + -18x + -10x2 = 15 + -15 + 25x + -25x + 10x2 + -10x2 Combine like terms: 15 + -15 = 0 -19 + -18x + -10x2 = 0 + 25x + -25x + 10x2 + -10x2 -19 + -18x + -10x2 = 25x + -25x + 10x2 + -10x2 Combine like terms: 25x + -25x = 0 -19 + -18x + -10x2 = 0 + 10x2 + -10x2 -19 + -18x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -19 + -18x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(19 + 18x + 10x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(19 + 18x + 10x2)' equal to zero and attempt to solve: Simplifying 19 + 18x + 10x2 = 0 Solving 19 + 18x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.9 + 1.8x + x2 = 0.0 Move the constant term to the right: Add '-1.9' to each side of the equation. 1.9 + 1.8x + -1.9 + x2 = 0.0 + -1.9 Reorder the terms: 1.9 + -1.9 + 1.8x + x2 = 0.0 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + 1.8x + x2 = 0.0 + -1.9 1.8x + x2 = 0.0 + -1.9 Combine like terms: 0.0 + -1.9 = -1.9 1.8x + x2 = -1.9 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = -1.9 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = -1.9 + 0.81 Combine like terms: -1.9 + 0.81 = -1.09 0.81 + 1.8x + x2 = -1.09 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = -1.09 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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